A Survey of High School Seniors from a Certain School $f ( x ) = \frac { 1 } { 13.5 \sqrt { 2 \pi } } e ^ { - ( x - 700 ) ^ { 2 } /3 64.5 }$

Multiple Choice

A survey of high school seniors from a certain school district who took the SAT has determined that the mean score on the mathematics portion was 700 with a standard deviation of 13.5. By a normal probability density function the data can be modeled as $f ( x ) = \frac { 1 } { 13.5 \sqrt { 2 \pi } } e ^ { - ( x - 700 ) ^ { 2 } /3 64.5 }$ . Find the derivative of the model.

A) $f ^ { \prime } ( x ) = \frac { - 2 \sqrt { 2 } ( x - 700 ) e ^ { - ( x -700 ) ^ { 2 } / 182.25 } } { 4,921 \sqrt { \pi } }$
B) $f ^ { \prime } ( x ) = \frac { - 2 \sqrt { 2 } ( x - 700 ) e ^ { - ( x -700 ) ^ { 2 } / 364.5 } } { 9,842 \sqrt { \pi } }$
C) $f ^ { \prime } ( x ) = \frac { \sqrt { 2 } ( x - 700 ) e ^ { - ( x - 700 ) ^ { 2 } / 364.5 } } { 4,921 \sqrt { \pi } }$
D) $f ^ { \prime } ( x ) = \frac { \sqrt { 2 } ( x - 700 ) e ^ { - ( x - 700 ) ^ { 2 } / 364.5 } } { 9,842 \sqrt { \pi } }$
E) $f ^ { \prime } ( x ) = \frac { \sqrt { 2 } ( x - 700 ) e ^ { - ( x - 70 ) ^ { 2 } / 182.25 } } { 4,921 \sqrt { \pi } }$